# Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Cross-Sections in the Molecular Frame: MFPADs

#### 2.2. LCAO B-Spline Code

#### 2.3. Computational Details

## 3. Results and Discussion

#### MFPAD Profiles

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Cherepkov, N.A.; Kuznetsov, V.V. Photoionization of oriented molecules. Z. Phys. D At. Mol. Clust.
**1987**, 7, 271–280. [Google Scholar] [CrossRef] - Chandra, N. Photoelectron spectroscopic studies of polyatomic molecules. I. Theory. J. Phys. B At. Mol. Phys.
**1987**, 20, 3405–3415. [Google Scholar] [CrossRef] - Reid, K.L. Photoelectron angular distributions: Developments in applications to isolated molecular systems. Mol. Phys.
**2012**, 110, 131–147. [Google Scholar] [CrossRef] - Stapelfeldt, H.; Seideman, T. Colloquium: Aligning molecules with strong laser pulses. Rev. Mod. Phys.
**2003**, 75, 543–557. [Google Scholar] [CrossRef][Green Version] - Dill, D. Fixed-molecule photoelectron angular distributions. J. Chem. Phys.
**1976**, 65, 1130–1133. [Google Scholar] [CrossRef] - Dill, D.; Siegel, J.; Dehmer, J.L. Spectral variation of fixed-molecule photoelectron angular distributions. J. Chem. Phys.
**1976**, 65, 3158–3160. [Google Scholar] [CrossRef] - Davenport, J.W. Ultraviolet Photoionization Cross Sections for N
_{2}and CO. Phys. Rev. Lett.**1976**, 36, 945–949. [Google Scholar] [CrossRef] - Dörner, R.; Mergel, V.; Jagutzki, O.; Spielberger, L.; Ullrich, J.; Moshammer, R.; Schmidt-Böcking, H. Cold Target Recoil Ion Momentum Spectroscopy: A ‘momentum microscope’ to view atomic collision dynamics. Phys. Rep.
**2000**, 330, 95–192. [Google Scholar] [CrossRef] - Borràs, V.J.; González-Vázquez, J.; Argenti, L.; Martín, F. Molecular-Frame Photoelectron Angular Distributions of CO in the Vicinity of Feshbach Resonances: An XCHEM Approach. J. Chem. Theory Comput.
**2021**, 17, 6330–6339. [Google Scholar] - Motoki, S.; Adachi, J.; Hikosaka, Y.; Ito, K.; Sano, M.; Soejima, K.; Yagishita, A.; Raseev, G.; Cherepkov, N.A. K-shell photoionization of CO: I. Angular distributions of photoelectrons from fixed-in-space molecules. J. Phys. At. Mol. Opt. Phys.
**2000**, 33, 4193–4212. [Google Scholar] [CrossRef] - Geßner, O.; Hikosaka, Y.; Zimmermann, B.; Hempelmann, A.; Lucchese, R.R.; Eland, J.H.D.; Guyon, P.-M.; Becker, U. 4σ
^{−1}Inner Valence Photoionization Dynamics of NO Derived from Photoelectron-Photoion Angular Correlations. Phys. Rev. Lett.**2002**, 88, 193002. [Google Scholar] [PubMed] - Cherepkov, N.A.; Semenov, S.K.; Hikosaka, Y.; Ito, K.; Motoki, S.; Yagishita, A. Manifestation of Many-Electron Correlations in Photoionization of the K Shell of N
_{2}. Phys. Rev. Lett.**2000**, 84, 250–253. [Google Scholar] [CrossRef] [PubMed] - Gregory, M.; Hockett, P.; Stolow, A.; Makhija, V. Towards molecular frame photoelectron angular distributions in polyatomic molecules from lab frame coherent rotational wavepacket evolution. J. Phys. B At. Mol. Opt. Phys.
**2021**, 54, 145601. [Google Scholar] [CrossRef] - Guillemin, R.; Decleva, P.; Stener, M.; Bomme, C.; Marin, T.; Journel, L.; Marchenko, T.; Kushawaha, R.K.; Jänkälä, K.; Trcera, N.; et al. Selecting core-hole localization or delocalization in CS2 by photofragmentation dynamics. Nat. Commun.
**2015**, 6, 6166. [Google Scholar] [CrossRef] [PubMed][Green Version] - Fukuzawa, H.; Lucchese, R.R.; Liu, X.-J.; Sakai, K.; Iwayama, H.; Nagaya, K.; Kreidi, K.; Schöffler, M.S.; Harries, J.R.; Tamenori, Y.; et al. Probing molecular bond-length using molecular-frame photoelectron angular distributions. J. Chem. Phys.
**2019**, 150, 174306. [Google Scholar] [CrossRef] [PubMed][Green Version] - Fukuzawa, H.; Yamada, S.; Sakakibara, Y.; Tachibana, T.; Ito, Y.; Takanashi, T.; Nishiyama, T.; Sakai, T.; Nagaya, K.; Saito, N.; et al. Probing gaseous molecular structure by molecular-frame photoelectron angular distributions. J. Chem. Phys.
**2019**, 151, 104302. [Google Scholar] [CrossRef] - Shigemasa, E.; Adachi, J.; Soejima, K.; Watanabe, N.; Yagishita, A.; Cherepkov, N.A. Direct Determination of Partial Wave Contributions in the σ* Shape Resonance of CO Molecules. Phys. Rev. Lett.
**1998**, 80, 1622–1625. [Google Scholar] [CrossRef] - Jahnke, T.; Weber, T.; Landers, A.L.; Knapp, A.; Schössler, S.; Nickles, J.; Kammer, S.; Jagutzki, O.; Schmidt, L.; Czasch, A.; et al. Circular Dichroism in K-Shell Ionization from Fixed-in-Space CO and N
_{2}Molecules. Phys. Rev. Lett.**2002**, 88, 73002. [Google Scholar] [CrossRef] - Motoki, S.; Adachi, J.; Ito, K.; Ishii, K.; Soejima, K.; Yagishita, A.; Semenov, S.K.; Cherepkov, N.A. Complete photoionization experiment in the region of the 2σ
_{g}→σ_{u}shape resonance of the N_{2}molecule. J. Phys. B At. Mol. Opt. Phys.**2002**, 35, 3801–3819. [Google Scholar] [CrossRef] - Lebech, M.; Houver, J.C.; Dowek, D.; Lucchese, R.R. Molecular Frame Photoelectron Emission in the Presence of Autoionizing Resonances. Phys. Rev. Lett.
**2006**, 96, 73001. [Google Scholar] [CrossRef] - Martín, F.; Fernández, J.; Havermeier, T.; Foucar, L.; Weber, T.; Kreidi, K.; Schöffler, M.; Schmidt, L.; Jahnke, T.; Jagutzki, O.; et al. Single photon-induced symmetry breaking of H
_{2}dissociation. Science**2007**, 315, 629–633. [Google Scholar] [CrossRef][Green Version] - Golovin, A.V.; Heiser, F.; Quayle, C.J.K.; Morin, P.; Simon, M.; Gessner, O.; Guyon, P.-M.; Becker, U. Observation of Site-Specific Electron Emission in the Decay of Superexcited O
_{2}. Phys. Rev. Lett.**1997**, 79, 4554–4557. [Google Scholar] [CrossRef] - Holzmeier, F.; Joseph, J.; Houver, J.C.; Lebech, M.; Dowek, D.; Lucchese, R.R. Influence of shape resonances on the angular dependence of molecular photoionization delays. Nat. Commun.
**2021**, 12, 7343. [Google Scholar] [CrossRef] - Rist, J.; Klyssek, K.; Novikovskiy, N.M.; Kircher, M.; Vela-Pérez, I.; Trabert, D.; Grundmann, S.; Tsitsonis, D.; Siebert, J.; Geyer, A.; et al. Measuring the photoelectron emission delay in the molecular frame. Nat. Commun.
**2021**, 12, 6657. [Google Scholar] [CrossRef] - Koch, C.P.; Lemeshko, M.; Sugny, D. Quantum control of molecular rotation. Rev. Mod. Phys.
**2019**, 91, 35005. [Google Scholar] [CrossRef][Green Version] - Boll, R.; Rouzée, A.; Adolph, M.; Anielski, D.; Aquila, A.; Bari, S.; Bomme, C.; Bostedt, C.; Bozek, J.D.; Chapman, H.N.; et al. Imaging molecular structure through femtosecond photoelectron diffraction on aligned and oriented gas-phase molecules. Faraday Discuss.
**2014**, 171, 57–80. [Google Scholar] [CrossRef][Green Version] - Ullrich, J.; Moshammer, R.; Dorn, A.; Dörner, R.; Schmidt, L.P.H.; Schmidt-Böcking, H. Recoil-ion and electron momentum spectroscopy: Reaction-microscopes. Rep. Prog. Phys.
**2003**, 66, 1463–1545. [Google Scholar] [CrossRef] - Kastirke, G.; Schöffler, M.S.; Weller, M.; Rist, J.; Boll, R.; Anders, N.; Baumann, T.M.; Eckart, S.; Erk, B.; De Fanis, A.; et al. Photoelectron Diffraction Imaging of a Molecular Breakup Using an X-ray Free-Electron Laser. Phys. Rev. X
**2020**, 10, 21052. [Google Scholar] [CrossRef] - Pier, A.; Fehre, K.; Grundmann, S.; Vela-Perez, I.; Strenger, N.; Kircher, M.; Tsitsonis, D.; Williams, J.B.; Senftleben, A.; Baumert, T.; et al. Chiral photoelectron angular distributions from ionization of achiral atomic and molecular species. Phys. Rev. Res.
**2020**, 2, 33209. [Google Scholar] [CrossRef] - Pérez-Torres, J.F.; Sanz-Vicario, J.L.; Veyrinas, K.; Billaud, P.; Picard, Y.J.; Elkharrat, C.; Poullain, S.M.; Saquet, N.; Lebech, M.; Houver, J.C.; et al. Circular dichroism in molecular-frame photoelectron angular distributions in the dissociative photoionization of H
_{2}and D_{2}molecules. Phys. Rev. A**2014**, 90, 43417. [Google Scholar] [CrossRef][Green Version] - Golovin, A.V.; Anielski, D.; Gordeev, S.V.; Lagodinski, V.M.; Chizhov, Y.V.; Küpper, J.; Rolles, D. The effect of elliptical polarization in MSXα calculations of the molecular-frame photoelectron angular distributions of CO C(1s) ionization. Eur. Phys. J. D
**2019**, 73, 131. [Google Scholar] [CrossRef] - Hockett, P.; Frumker, E.; Villeneuve, D.M.; Corkum, P.B. Time delay in molecular photoionization. J. Phys. B At. Mol. Opt. Phys.
**2016**, 49, 95602. [Google Scholar] [CrossRef] - Dowek, D.; Lucchese, R.R. Photoionization dynamics: Photoemission in the molecular frame of small molecules ionized by linearly and elliptically polarized light. In Dynamical Processes in Atomic and Molecular Physics; Ogurtsov, G., Dowek, D., Eds.; Bentham Science Publishers: Sharjah, United Arab Emirates, 2012; pp. 57–95. [Google Scholar]
- Squibb, R.J.; Sapunar, M.; Ponzi, A.; Richter, R.; Kivimäki, A.; Plekan, O.; Finetti, P.; Sisourat, N.; Zhaunerchyk, V.; Marchenko, T.; et al. Acetylacetone photodynamics at a seeded free-electron laser. Nat. Commun.
**2018**, 9, 63. [Google Scholar] [CrossRef] [PubMed] - Ponzi, A.; Angeli, C.; Cimiraglia, R.; Coriani, S.; Decleva, P. Dynamical photoionization observables of the CS molecule: The role of electron correlation. J. Chem. Phys.
**2014**, 140, 204304. [Google Scholar] [CrossRef] - Ponzi, A.; Sapunar, M.; Angeli, C.; Cimiraglia, R.; Došlić, N.; Decleva, P. Photoionization of furan from the ground and excited electronic states. J. Chem. Phys.
**2016**, 144, 84307. [Google Scholar] [CrossRef] - Toffoli, D.; Stener, M.; Fronzoni, G.; Decleva, P. Convergence of the multicenter B-spline DFT approach for the continuum. Chem. Phys.
**2002**, 276, 25–43. [Google Scholar] [CrossRef] - Te Velde, G.; Bickelhaupt, F.M.; Baerends, E.J.; Guerra, C.F.; van Gisbergen, S.J.A.; Snijders, J.G.; Ziegler, T. Chemistry with ADF. J. Comput. Phys.
**2001**, 22, 931–967. [Google Scholar] [CrossRef] - ADF2016. SCM, Theoretical Chemistry. Vrije Universiteit, Amsterdam, The Netherlands. Available online: https://www.scm.com/doc.2016/ADF/index.html (accessed on 20 February 2022).
- Brosolo, M.; Decleva, P.; Lisini, A. Continuum wavefunctions calculations with least-squares schemes in a B-splines basis. Comput. Phys. Commun.
**1992**, 71, 207–214. [Google Scholar] [CrossRef] - Van Leeuwen, R.; Baerends, E.J. Exchange-correlation potential with correct asymptotic behavior. Phys. Rev. A
**1994**, 49, 2421–2431. [Google Scholar] [CrossRef][Green Version] - Stener, M.; Furlan, S.; Decleva, P. Density functional calculations of photoionization with an exchange-correlation potential with the correct asymptotic behaviour. J. Phys. B At. Mol. Opt. Phys.
**2000**, 33, 1081–1102. [Google Scholar] [CrossRef] - Ponzi, A.; Quadri, N.; Angeli, C.; Decleva, P. Electron correlation effects in the photoionization of CO and isoelectronic diatomic molecules. Phys. Chem. Chem. Phys.
**2019**, 21, 1937–1951. [Google Scholar] [CrossRef] [PubMed] - Piteša, T.; Sapunar, M.; Ponzi, A.; Gelin, M.F.; Došlić, N.; Domcke, W.; Decleva, P. Combined Surface-Hopping, Dyson orbital, and B-Spline approach for the computation of time-resolved photoelectron spectroscopy signals: The internal conversion in pyrazine. J. Chem. Theory Comput.
**2021**, 17, 5098–5109. [Google Scholar] [CrossRef] [PubMed] - Werner, H.-J.; Knowles, P.J.; Knizia, G.; Manby, F.R.; Schutz, M. MOLPRO, Version 2010.1, a Package of Ab Initio Programs. Available online: http://wild.life.nctu.edu.tw/~jsyu/compchem/molpro-2010.1-manual.pdf (accessed on 20 February 2022).

**Figure 1.**Electronic configurations of the S${}_{1}$, T${}_{2}$ (

**a**) and S${}_{2}$, T${}_{1}$ (

**b**) excited states of acetylacetone with the plots of the three outer valence molecular orbitals calculated with CASSCF/cc-pVDZ.

**Figure 2.**Selected coefficients of the Dyson orbitals expressed in the AO basis together with the Dyson orbital plots (CASSCF/cc-pVDZ) for the ionization from the excited states involved in the photodynamics process of acetylacetone.

**Figure 3.**Computed MFPADs for the photoionization from the S${}_{1}$ (

**a**), T${}_{1}$ (

**b**), and T${}_{2}$ (

**c**) excited states of acetylacetone to the corresponding first ionic state, at the selected kinetic energy of 6.04 eV. The electric field is oriented along the x axis. Orientation of the molecule is also shown on top of figure (x, y, z axes are, respectively, identified by red, green and blue colors).

**Figure 4.**Computed MFPADs for the photoionization from the S${}_{1}$ (

**a**), T${}_{1}$ (

**b**), and T${}_{2}$ (

**c**) excited states of acetylacetone to the corresponding first ionic state, at the selected kinetic energy of 6.04 eV. The electric field is oriented along the y-axis. Orientation of the molecule is also shown on top of figure (x, y, z axes are, respectively, identified by red, green and blue colors).

**Table 1.**Experimental and theoretical ionization energies (IE) of acetylacetone to the first ionic state (in eV) for the investigated transitions.

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**MDPI and ACS Style**

Ponzi, A.; Sapunar, M.; Došlić, N.; Decleva, P. Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions. *Molecules* **2022**, *27*, 1811.
https://doi.org/10.3390/molecules27061811

**AMA Style**

Ponzi A, Sapunar M, Došlić N, Decleva P. Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions. *Molecules*. 2022; 27(6):1811.
https://doi.org/10.3390/molecules27061811

**Chicago/Turabian Style**

Ponzi, Aurora, Marin Sapunar, Nadja Došlić, and Piero Decleva. 2022. "Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions" *Molecules* 27, no. 6: 1811.
https://doi.org/10.3390/molecules27061811